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In mathematics, the Airy function Ai(x) is a special function, i.e., a function that appears so frequently that it deserves its own name.
Although the function is not strictly integrable (the integrand does not decay as t → ∞), the integral converges because of the positive and negative parts of the rapid oscillations tend to cancel one another out (this can be checked by integration by parts).
The Airy function is named after the British astronomer George Biddell Airy, who encountered it in his study of optics (Airy 1838).
The width of the airy disk is used to define the theoretical maximum resolution for an optical system (defined as the diameter of the first dark circle).
When the diameter of the airy disk's central peak becomes large relative to the pixel size in the camera (or maximum tolerable circle of confusion), it begins to have a visual impact on the image.
This is because the airy disks are only partially overlapping, similar to the effect on adjacent rows of alternating fl and white airy disks (as shown on the right).
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